A photocathode whose work function is 2.6 eV is illuminated with white light tha

Question

A photocathode whose work function is 2.6 eV is illuminated with white light that has a continuous wavelength band from 400 nm to 700 nm. The range of the wavelength band in this white light illumination for which photoelectrons are not produced, in nm, is closest to:

A photocathode whose work function is 2.6 eV is illuminated with white light that has a continuous wavelength band from 400 nm to 700 nm. The range of the wavelength band in this white light illumination for which photoelectrons are not produced, in nm, is closest to:

Explanation / Answer

Photoelectrons will NOT be produced if the photon energy is less than the work function.

Photon energy = hf = hc/ {Note that bigger means less energy}

where h is Planck's constant; c is the speed of light; is the wavelength.

{Instead of converting everything into joules, we'll use : h = 4.14 * 10^-15 eV.s}

At the point where photoelectrons are just about to be emitted:
2.6 = (4.14 * 10^-15) * (3 * 10^8) /

= (4.14 * 10^-15) * (3 * 10^8) / 2.6
= 4.777 * 10^-7 m
= 480 nm (approximated)

So wavelengths longer than 480 nm will NOT produce photoelectrons
That looks like answer (D) to me.

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